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Journal articles on the topic 'Algebraic difference equation'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Arreche, Carlos E. "Computation of the difference-differential Galois group and differential relations among solutions for a second-order linear difference equation." Communications in Contemporary Mathematics 19, no. 06 (2017): 1650056. http://dx.doi.org/10.1142/s0219199716500565.

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We apply the difference-differential Galois theory developed by Hardouin and Singer to compute the differential-algebraic relations among the solutions to a second-order homogeneous linear difference equation [Formula: see text] where the coefficients [Formula: see text] are rational functions in [Formula: see text] with coefficients in [Formula: see text]. We develop algorithms to compute the difference-differential Galois group associated to such an equation, and show how to deduce the differential-algebraic relations among the solutions from the defining equations of the Galois group.

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2

Malykh, Mikhail, and Leonid Sevastianov. "Finite Difference Schemes as Algebraic Correspondences between Layers." EPJ Web of Conferences 173 (2018): 03016. http://dx.doi.org/10.1051/epjconf/201817303016.

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For some differential equations, especially for Riccati equation, new finite difference schemes are suggested. These schemes define protective correspondences between the layers. Calculation using these schemes can be extended to the area beyond movable singularities of exact solution without any error accumulation.

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3

Skovpen, Sergey Mikhailovich, and Albert Saitovich Iskhakov. "Exact Solution of a Linear Difference Equation in a Finite Number of Steps." JOURNAL OF ADVANCES IN MATHEMATICS 14, no. 1 (2018): 7560–63. http://dx.doi.org/10.24297/jam.v14i1.7206.

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An exact solution of a linear difference equation in a finite number of steps has been obtained. This refutes the conventional wisdom that a simple iterative method for solving a system of linear algebraic equations is approximate. The nilpotency of the iteration matrix is the necessary and sufficient condition for getting an exact solution. The examples of iterative equations providing an exact solution to the simplest algebraic system are presented.

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4

A.S., Iskhakov, and Skovpen S.M. "Exact Solution of a Linear Difference Equation in a Finite Number of Steps." Journal of Progressive Research in Mathematics 13, no. 2 (2018): 2259–62. https://doi.org/10.5281/zenodo.3974630.

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An exact solution of a linear difference equation in a finite number of steps has been obtained. This refutes the conventional wisdom that a simple iterative method for solving a system of linear algebraic equations is approximate. The nilpotency of the iteration matrix is the necessary and sufficient condition for getting an exact solution. The examples of iterative equations providing an exact solution to the simplest algebraic system are presented.

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5

Wang, Fang, Yuxue Chen, and Yuting Liu. "Finite Difference and Chebyshev Collocation for Time-Fractional and Riesz Space Distributed-Order Advection–Diffusion Equation with Time-Delay." Fractal and Fractional 8, no. 12 (2024): 700. http://dx.doi.org/10.3390/fractalfract8120700.

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In this paper, we have established a numerical method for a class of time-fractional and Riesz space distributed-order advection–diffusion equation with time-delay. Firstly, we transform the Riesz space distributed-order derivative term of the diffusion equation into multi-term fractional derivatives by using the Gauss quadrature formula. Secondly, we discretize time by using second-order finite differences, discretize space by using second kind Chebyshev polynomials, and convert the multi-term fractional equation to a system of algebraic equations. Finally, we solve the algebraic equations by

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6

Zheng, Xiu-Min, Zong-Xuan Chen, and Tu Jin. "Growth of meromorphic solutions of some difference equations." Applicable Analysis and Discrete Mathematics 4, no. 2 (2010): 309–21. http://dx.doi.org/10.2298/aadm100512022z.

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We investigate higher order difference equations and obtain some results on the growth of transcendental meromorphic solutions, which are complementary to the previous results. Examples are also given to show the sharpness of these results. We also investigate the growth of transcendental entire solutions of a homogeneous algebraic difference equation by using the difference analogue of Wiman-Valiron Theory.

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7

DOBREV, V. K., H. D. DOEBNER, and C. MRUGALLA. "DIFFERENCE ANALOGUES OF THE FREE SCHRÖDINGER EQUATION." Modern Physics Letters A 14, no. 17 (1999): 1113–22. http://dx.doi.org/10.1142/s021773239900119x.

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We propose an infinite family of difference equations, which are derived from the first principle that they are invariant with respect to the Schrödinger algebra. The first member of this family is a difference analogue of the free Schrödinger equation. These equations are obtained via a purely algebraic construction from a corresponding family of singular vectors in Verma modules over the Schrödinger algebra. The crucial moment in the construction is the realization of the Schrödinger algebra through additive difference vector fields, i.e. vector fields with difference operators instead of di

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8

Suliman, Tammam, Uta Berger, Marieke Van der Maaten-Theunissen, Ernst Van der Maaten, and Wael Ali. "Modeling dominant height growth using permanent plot data for Pinus brutia stands in the Eastern Mediterranean region." Forest Systems 30, no. 1 (2021): eSC03. http://dx.doi.org/10.5424/fs/2021301-17687.

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Aim of the study: At current, forest management in the Eastern Mediterranean region is largely based on experience rather than on management plans. To support the development of such plans, this study develops and compares site index equations for pure even-aged Pinus brutia stands in Syria using base-age invariant techniques that realistically describe dominant height growth.Materials and methods: Data on top height and stand age were obtained in 2008 and 2016 from 80 permanent plots capturing the whole range of variation in site conditions, stand age and stand density. Both the Algebraic Dif

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9

Zhang, Xiaojing, Vladimir Gerdt, and Yury Blinkov. "Algebraic Construction of a Strongly Consistent, Permutationally Symmetric and Conservative Difference Scheme for 3D Steady Stokes Flow." Symmetry 11, no. 2 (2019): 269. http://dx.doi.org/10.3390/sym11020269.

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By using symbolic algebraic computation, we construct a strongly-consistent second-order finite difference scheme for steady three-dimensional Stokes flow and a Cartesian solution grid. The scheme has the second order of accuracy and incorporates the pressure Poisson equation. This equation is the integrability condition for the discrete momentum and continuity equations. Our algebraic approach to the construction of difference schemes suggested by the second and the third authors combines the finite volume method, numerical integration, and difference elimination. We make use of the technique

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10

Altürk, Ahmet. "Application of the Bernstein polynomials for solving Volterra integral equations with convolution kernels." Filomat 30, no. 4 (2016): 1045–52. http://dx.doi.org/10.2298/fil1604045a.

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In this article, we consider the second-type linear Volterra integral equations whose kernels based upon the difference of the arguments. The aim is to convert the integral equation to an algebraic one. This is achieved by approximating functions appearing in the integral equation with the Bernstein polynomials. Since the kernel is of convolution type, the integral is represented as a convolution product. Taylor expansion of kernel along with the properties of convolution are used to represent the integral in terms of the Bernstein polynomials so that a set of algebraic equations is obtained.

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11

Heydari, Marzieh, Mehdi Ghovatmand, Mohammad Hadi Noori Skandari, and Dumitru Baleanu. "An Efficient Convergent Approach for Difference Delayed Reaction-Diffusion Equations." European Journal of Pure and Applied Mathematics 17, no. 3 (2024): 1565–84. http://dx.doi.org/10.29020/nybg.ejpam.v17i3.5197.

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It is usually not possible to solve partial differential equations, especially the delay type, with analytical methods. Therefore, in this article, we present an efficient method for solving differential equations of the difference delayed reaction-diffusion type, which can be generalized to other delayed partial differential equations. In the proposed approach, we first convert the delayed equation into an equivalent non-delayed equation by inserting the corresponding delay function with an effective technique. Then, using a pseudo-spectral method, we discretize the obtained equation in the L

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12

Chen, S. G., A. G. Ulsoy, and Y. Koren. "Computational Stability Analysis of Chatter in Turning." Journal of Manufacturing Science and Engineering 119, no. 4A (1997): 457–60. http://dx.doi.org/10.1115/1.2831174.

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Machine tool chatter is one of the major constraints that limits productivity of the turning process. It is a self-excited vibration that is mainly caused by the interaction between the machine-tool/workpiece structure and the cutting process dynamics. This work introduces a general method which avoids lengthy algebraic (symbolic) manipulations in deriving, a characteristic equation. The solution scheme is simple and robust since the characteristic equation is numerically formulated as a single variable equation whose variable is well bounded rather than two nonlinear algebraic equations with

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13

LALLEMAND, PIERRE, and LI-SHI LUO. "HYBRID FINITE-DIFFERENCE THERMAL LATTICE BOLTZMANN EQUATION." International Journal of Modern Physics B 17, no. 01n02 (2003): 41–47. http://dx.doi.org/10.1142/s0217979203017060.

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We analyze the acoustic and thermal properties of athermal and thermal lattice Boltzmann equation (LBE) in 2D and show that the numerical instability in the thermal lattice Boltzmann equation (TLBE) is related to the algebraic coupling among different modes of the linearized evolution operator. We propose a hybrid finite-difference (FD) thermal lattice Boltzmann equation (TLBE). The hybrid FD-TLBE scheme is far superior over the existing thermal LBE schemes in terms of numerical stability. We point out that the lattice BGK equation is incompatible with the multiple relaxation time model.

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14

Du, Nguyen Huu, and Nguyen Chi Liem. "LINEAR TRANSFORMATIONS AND FLOQUET THEOREM FOR LINEAR IMPLICIT DYNAMIC EQUATIONS ON TIME SCALES." Asian-European Journal of Mathematics 06, no. 01 (2013): 1350004. http://dx.doi.org/10.1142/s1793557113500046.

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This paper is concerned with Cauchy problem, Lyapunov transformations, Floquet and Lyapunov theorems for linear implicit dynamic equation AtxΔ= Btx with index-1 on time scales. The stability of this equation under the act of these Lyapunov transformations is also considered. The results are a unification and generalization of previous results for differential-algebraic equations and implicit difference systems.

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15

Martinsson, Per-Gunnar, and Gregory J. Rodin. "Boundary algebraic equations for lattice problems." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2108 (2009): 2489–503. http://dx.doi.org/10.1098/rspa.2008.0473.

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Procedures for constructing boundary integral equations equivalent to linear boundary-value problems governed by partial differential equations are well established. In this paper, it is demonstrated how these procedures can be extended to linear boundary-value problems defined on lattices and governed by algebraic (‘difference’) equations. The boundary equations that arise are then themselves algebraic equations. Such ‘boundary algebraic equations’ (BAEs) are derived for fundamental boundary-value problems defined on both perfect lattices and lattices with defects. It is demonstrated that key

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16

Jalius, Chriscella, and Zanariah Abdul Majid. "Numerical Solution of Second-Order Fredholm Integrodifferential Equations with Boundary Conditions by Quadrature-Difference Method." Journal of Applied Mathematics 2017 (2017): 1–5. http://dx.doi.org/10.1155/2017/2645097.

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In this research, the quadrature-difference method with Gauss Elimination (GE) method is applied for solving the second-order of linear Fredholm integrodifferential equations (LFIDEs). In order to derive an approximation equation, the combinations of Composite Simpson’s 1/3 rule and second-order finite-difference method are used to discretize the second-order of LFIDEs. This approximation equation will be used to generate a system of linear algebraic equations and will be solved by using Gauss Elimination. In addition, the formulation and the implementation of the quadrature-difference method

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17

Cieszewski, C. J. "Comparing Fixed- and Variable-Base-Age Site Equations Having Single Versus Multiple Asymptotes." Forest Science 48, no. 1 (2002): 7–23. http://dx.doi.org/10.1093/forestscience/48.1.7.

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Abstract Site equations compute values of a variable Y as a function of both variable t and a value of the variable Y = Y0 measured at an arbitrary t = t0. For example, the plant size (Y) can be defined as a function of both age (t) and a reference size (Y0) measured at the base age t0. The base age can be implicit (i.e., implied but hidden), as in fixed-base-age equations [e.g., Y = f(t, S), where S is Y at t = 50], or explicit (i.e., readily exposed and changeable), as in dynamic equations [e.g., Y = f(t, t0, Y0)]. Using as the main criterion the ability of an equation to generate concurrent

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18

CAI, Q. D. "CONTINUOUS NEWTON METHOD FOR NONLINEAR PARTIAL DIFFERENTIAL EQUATION." Modern Physics Letters B 24, no. 13 (2010): 1303–6. http://dx.doi.org/10.1142/s0217984910023487.

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Newton method is a widely used iteration method in solving nonlinear algebraic equations. In this method, a linear algebraic equations need to be solved in every step. The coefficient matrix of the algebraic equations is so-called Jacobian matrix, which needs to be determined at every step. For a complex non-linear system, usually no explicit form of Jacobian matrix can be found. Several methods are introduced to obtain an approximated matrix, which are classified as Jacobian-free method. The finite difference method is used to approximate the derivatives in Jacobian matrix, and a small parame

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19

Bankmann, Daniel, and Matthias Voigt. "On linear-quadratic optimal control of implicit difference equations." IMA Journal of Mathematical Control and Information 36, no. 3 (2018): 779–833. http://dx.doi.org/10.1093/imamci/dny007.

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Abstract In this work we investigate explicit and implicit difference equations and the corresponding infinite time horizon linear-quadratic optimal control problem. We derive conditions for feasibility of the optimal control problem as well as existence and uniqueness of optimal controls under certain weaker assumptions compared to the standard approaches in the literature which are using algebraic Riccati equations. To this end, we introduce and analyse a discrete-time Lur’e equation and a corresponding Kalman–Yakubovich–Popov (KYP) inequality. We show that solvability of the KYP inequality

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20

Talaei, Younes, Hasan Hosseinzadeh, and Samad Noeiaghdam. "A Finite Difference-Spectral Method for Solving the European Call Option Black–Scholes Equation." Mathematical Modelling of Engineering Problems 8, no. 2 (2021): 273–78. http://dx.doi.org/10.18280/mmep.080215.

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In this paper, we present a novel technique based on backward-difference method and Galerkin spectral method for solving Black–Scholes equation. The main propose of this method is to reduce the solution of this problem to the solution of a system of algebraic equations. The convergence order of the proposed method is investigated. Also, we provide numerical experiment to show the validity of proposed method.

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21

Berikelashvili, Givi, and Manana Mirianashvili. "On the convergence of difference schemes for the generalized BBM–Burgers equation." Georgian Mathematical Journal 26, no. 3 (2019): 341–49. http://dx.doi.org/10.1515/gmj-2018-0075.

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Abstract A three-level finite difference scheme is studied for the initial-boundary value problem of the generalized Benjamin–Bona–Mahony–Burgers equation. The obtained algebraic equations are linear with respect to the values of the desired function for each new level. The unique solvability and absolute stability of the difference scheme are shown. It is proved that the scheme is convergent with the rate of order {k-1} when the exact solution belongs to the Sobolev space {W_{2}^{k}(Q)} , {1<k\leq 3} .

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22

Dong, Ming, and Theodore Simos. "A new high algebraic order efficient finite difference method for the solution of the Schrödinger equation." Filomat 31, no. 15 (2017): 4999–5012. http://dx.doi.org/10.2298/fil1715999d.

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The development of a new five-stages symmetric two-step method of fourteenth algebraic order with vanished phase-lag and its first, second, third and fourth derivatives is analyzed in this paper. More specifically: (1) we will present the development of the new method, (2) we will determine the local truncation error (LTE) of the new proposed method, (3) we will analyze the local truncation error based on the radial time independent Schr?dinger equation, (4) we will study the stability and the interval of periodicity of the new proposed method based on a scalar test equation with frequency dif

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23

Fakheri, Ahmad. "A General Expression for the Determination of the Log Mean Temperature Correction Factor for Shell and Tube Heat Exchangers." Journal of Heat Transfer 125, no. 3 (2003): 527–30. http://dx.doi.org/10.1115/1.1571078.

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This paper presents a single closed form algebraic equation for the determination of the Log Mean Temperature Difference correction factor F for shell and tube heat exchangers having N shell passes and 2M tube passes per shell. The equation and its graphical presentation generalize the traditional equations and charts used for the determination of F. The equation presented is also useful in design, analysis and optimization of multi shell and tube heat exchanger, particularly for direct determination of the number of shells.

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24

Li, Ruomeng, Jingru Geng, and Xianguo Geng. "Breather and rogue-wave solutions of the semi-discrete and continuous nonlinear Schrödinger equations on theta-function backgrounds." Nonlinearity 38, no. 1 (2024): 015012. https://doi.org/10.1088/1361-6544/ad9794.

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Abstract A new method to construct localized-wave solutions of the semi-discrete and continuous nonlinear Schrödinger (sd-NLS) equations on theta-function backgrounds simultaneously is developed. (1) The semi-discrete NLS equation is rewritten as the difference-quotient NLS equation so that the continuum limits are easy to calculate. (2) By rewriting the difference-quotient equation in the form of Hiorta bilinear equations, a theta-function seed solution for the difference-quotient NLS equation is derived, in which the theta-function is so general that both dn - and cn -type seed solutions are

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25

Simos, T. E. "High Algebraic Order Methods with Minimal Phase-Lag for Accurate Solution of the Schrödinger Equation." International Journal of Modern Physics C 09, no. 07 (1998): 1055–71. http://dx.doi.org/10.1142/s0129183198000996.

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A family of new hybrid four-step tenth algebraic order methods with phase-lag of order fourteen is developed for accurate computations of the radial Schrödinger equation. Numerical results obtained for the integration of the phase shift problem for the well known case of the Lennard-Jones potential and for the numerical solution of the coupled equations arising from the Schrödinger equation show that these new methods are better than other finite difference methods.

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26

EBERT, UTE, WIM VAN SAARLOOS, and BERT PELETIER. "Universal algebraic convergence in time of pulled fronts: the common mechanism for difference-differential and partial differential equations." European Journal of Applied Mathematics 13, no. 1 (2002): 53–66. http://dx.doi.org/10.1017/s0956792501004673.

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We analyze the front structures evolving under the difference-differential equation ∂tCj = −Cj+C2j−1 from initial conditions 0 [les ] Cj(0) [les ] 1 such that Cj(0) → 1 as j → ∞ suffciently fast. We show that the velocity v(t) of the front converges to a constant value v* according to v(t) = v*−3/(2λ*t)+(3√π/2) Dλ*/(λ*2Dt)3/2+[Oscr ](1/t2). Here v*, λ* and D are determined by the properties of the equation linearized around Cj = 1. The same asymptotic expression is valid for fronts in the nonlinear diffusion equation, where the values of the parameters λ*, v* and D are specific to the equation

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27

ARTEMYEV, Victor, Sergey MOKRUSHIN, Sergey SAVOSTIN, Artem MEDVEDEV, and Vitaly PANKOV. "PROCESSING OF TIME SIGNALS IN A DISCRETE TIME DOMAIN." Machine Science Journal 1, no. 1 (2023): 46–54. http://dx.doi.org/10.61413/frcr4965.

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This article is devoted to the processing of time signals in a discrete time domain. Time signals are the main object of analysis in many areas, such as signal processing, communication, control and much more. Today, for efficient signal processing, it is necessary to use methods adapted to the discrete time domain, using the Z-transform method to solve difference equations in the discrete time domain. The Ztransform method is a powerful and most effective tool for analyzing and solving difference equations, widely used in control systems, signal processing and other fields. The main steps of

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28

Khalaf Hussain, Ali. "Transient-False Method for Solving System of Nonlinear Partial Differential Equations." Journal of Education College Wasit University 1, no. 25 (2018): 509–22. http://dx.doi.org/10.31185/eduj.vol1.iss25.137.

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In this paper we study the false transient method to solve and transform a system of non-linear partial differential equations which can be solved using finite-difference method and give some problems which have a good results compared with the exact solution, whereas this method was used to transform the nonlinear partial differential equation to a linear partial differential equation which can be solved by using the alternating-direction implicit method after using the ADI method. The system of linear algebraic equations could be obtained and can be solved by using MATLAB.

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Leinartas, Evgenij, and Tat’jana Yakovleva. "Generating Function of the Solution of a Difference Equation and the Newton Polyhedron of the Characteristic Polynomial." Bulletin of Irkutsk State University. Series Mathematics 40 (2022): 3–14. http://dx.doi.org/10.26516/1997-7670.2022.40.3.

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Generating functions and difference equations are a powerful tool for studying problems of enumerative combinatorial analysis. In the one-dimensional case, the space of solutions of the difference equation is finite-dimensional. In the transition to a multidimensional situation, problems arise related both to the possibility of various options for specifying additional conditions on the solution of a difference equation (the Cauchy problem) and to describing the corresponding space of generating functions. For difference equations in rational cones of an integer lattice, sufficient conditions

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YUAN, ZHIJIANG, LIANGAN JIN, WEI CHI, and HENGDOU TIAN. "FINITE DIFFERENCE METHOD FOR SOLVING THE NONLINEAR DYNAMIC EQUATION OF UNDERWATER TOWED SYSTEM." International Journal of Computational Methods 11, no. 04 (2014): 1350060. http://dx.doi.org/10.1142/s0219876213500606.

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A wide body of work exists that describes numerical solution for the nonlinear system of underwater towed system. Many researchers usually divide the tow cable with less number elements for the consideration of computational time. However, this type of installation affects the accuracy of the numerical solution. In this paper, a newly finite difference method for solving the nonlinear dynamic equations of the towed system is developed. The mathematical model of tow cable and towed body are both discretized to nonlinear algebraic equations by center finite difference method. A newly discipline

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Ndayisenga, Serge, Leonid A. Sevastianov, and Konstantin P. Lovetskiy. "Finite-difference methods for solving 1D Poisson problem." Discrete and Continuous Models and Applied Computational Science 30, no. 1 (2022): 62–78. http://dx.doi.org/10.22363/2658-4670-2022-30-1-62-78.

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The paper discusses the formulation and analysis of methods for solving the one-dimensional Poisson equation based on finite-difference approximations - an important and very useful tool for the numerical study of differential equations. In fact, this is a classical approximation method based on the expansion of the solution in a Taylor series, based on which the recent progress of theoretical and practical studies allowed increasing the accuracy, stability, and convergence of methods for solving differential equations. Some of the features of this analysis include interesting extensions to cl

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Raslan, K. R., Khalid K. Ali, Reda Gamal Ahmed, Hind K. Al-Jeaid, and Amira Abd-Elall Ibrahim. "Study of Nonlocal Boundary Value Problem for the Fredholm–Volterra Integro-Differential Equation." Journal of Function Spaces 2022 (February 7, 2022): 1–16. http://dx.doi.org/10.1155/2022/4773005.

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In this paper, the existence and uniqueness of the Fredholm–Volterra integro-differential equation with the nonlocal condition will be studied. Also, we study the continuous dependence of the initial data. The numerical solution of the problem will be studied using the central difference approximations and trapezoidal rule to transform the Volterra–Fredholm integro-differential equation into a system of algebraic equations which can be solved together to get the solution. Finally, we solve some examples numerically to show the accuracy of the proposed method.

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Godongwana, B., D. Solomons, and M. S. Sheldon. "A Finite-Difference Solution of Solute Transport through a Membrane Bioreactor." Mathematical Problems in Engineering 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/810843.

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The current paper presents a theoretical analysis of the transport of solutes through a fixed-film membrane bioreactor (MBR), immobilised with an active biocatalyst. The dimensionless convection-diffusion equation with variable coefficients was solved analytically and numerically for concentration profiles of the solutes through the MBR. The analytical solution makes use of regular perturbation and accounts for radial convective flow as well as axial diffusion of the substrate species. The Michaelis-Menten (or Monod) rate equation was assumed for the sink term, and the perturbation was extende

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Rysbaiuly, B., and N. Rysbaeva. "THE METHOD OF SOLVING NONLINEAR HEAT TRANSFER MODEL IN FREEZING SOIL." EURASIAN JOURNAL OF MATHEMATICAL AND COMPUTER APPLICATIONS 8, no. 4 (2020): 83–96. http://dx.doi.org/10.32523/2306-6172-2020-8-4-83-96.

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The nonlinear model of heat transfer in freezing soil was corrected using the results of experimental studies of other scientists. A nonlinear difference equation is constructed and a priori estimates are obtained for solving nonlinear algebraic equations. The nonlinear difference problem is solved by Newton’s method. The paper also considers the problem of choosing the initial approximation of Newton’s method. Using a priori estimates, the quadratic convergence of the iterative method is proved. Numerical calculations have been performed. A strong discrepancy in results between linear and non

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Solonukha, O. V. "On the existence of time-periodic solutions of nonlinear parabolic differential equations with nonlocal boundary conditions of the Bitsadze-Samarskii type." Contemporary Mathematics. Fundamental Directions 69, no. 4 (2023): 712–25. http://dx.doi.org/10.22363/2413-3639-2023-69-4-712-725.

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We study a nonlinear parabolic differential equation in a bounded multidimensional domain with nonlocal boundary conditions of the Bitsadze-Samarskii type. We prove existence theorems for a periodic in time generalized solution. Su cient conditions for the existence of generalized solutions contain either an algebraic ellipticity condition or an algebraic strong ellipticity condition for the auxiliary differential-difference operator.

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Anta, Marcos Barrio, Fernando Castedo Dorado, Ulises Diéguez-Aranda, Juan G. Álvarez González, Bernard R. Parresol, and Roque Rodríguez Soalleiro. "Development of a basal area growth system for maritime pine in northwestern Spain using the generalized algebraic difference approach." Canadian Journal of Forest Research 36, no. 6 (2006): 1461–74. http://dx.doi.org/10.1139/x06-028.

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A basal area growth system for single-species, even-aged maritime pine (Pinus pinaster Ait.) stands in Galicia (northwestern Spain) was developed from data of 212 plots measured between one and four times. Six dynamic equations were considered for analysis, and both numerical and graphical methods were used to compare alternative models. The double cross-validation approach was used to assess the predictive ability of the models. The data were best described by a dynamic equation derived from the Korf growth function using the generalized algebraic difference approach (GADA) by considering two

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Agboola, Olasunmbo O., Talib Eh Elaikh, Jimevwo G. Oghonyon, and Olajide Ibikunle. "Effect of Mass per Unit Length on freely vibrating Simply Supported Rayleigh Beam." WSEAS TRANSACTIONS ON FLUID MECHANICS 17 (October 13, 2022): 173–80. http://dx.doi.org/10.37394/232013.2022.17.17.

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In this paper, free vibration characteristics of a uniform Rayleigh beam are studied using the differential transform method. The procedure entails transforming the partial differential equation governing the motion of the beam under consideration and the associated boundary conditions. The transformation yields a set of difference equations. Some simple algebraic operations are performed on the resulting difference equations to determine any ith natural frequency and the closed-form series function for any ith mode shape. Finally, one problem is presented to illustrate the implementation of t

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Tamizhmani, K. M., S. Kanagavel, B. Grammaticos, and A. Ramani. "Singularity structure and algebraic properties of the differential-difference Kadomtsev–Petviashvili equation." Chaos, Solitons & Fractals 11, no. 9 (2000): 1423–31. http://dx.doi.org/10.1016/s0960-0779(99)00059-4.

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Hameed, Amal S., and Radhi A. Zaboon. "Approximate Solutions for Optimal Control of Fixed Boundary Value Problems Using Variational and Minimum Approaches." Al-Mustansiriyah Journal of Science 34, no. 3 (2023): 72–85. http://dx.doi.org/10.23851/mjs.v34i3.1104.

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The optimal control is the process of finding a control strategy that extreme some performance index for a dynamic system (partial differential equation) over the class of admissibility. The present work deals with a problem of fixed boundary with a control manipulated in the structure of the partial differential equation. An attractive computational method for determining the optimal control of unconstrained linear dynamic system with a quadratic performance index is presented. In the proposed method the difference between every state variable and its initial condition is represented by a fin

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Kamel, Al-Khaled. "Sinc collocation linked with finite differences for Korteweg-de Vries Fractional Equation." International Journal of Electrical and Computer Engineering (IJECE) 10, no. 1 (2020): 512–20. https://doi.org/10.11591/ijece.v10i1.pp512-520.

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A novel numerical method is proposed for Korteweg-de Vries Fractional Equation. The fractional derivatives are described based on the Caputo sense. We construct the solution using different approach, that is based on using collocation techniques. The method combining a finite difference approach in the time-fractional direction, and the Sinc-Collocation in the space direction, where the derivatives are replaced by the necessary matrices, and a system of algebraic equations is obtained to approximate solution of the problem. The numerical results are shown to demonstrate the efficiency of the n

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Başhan, Ali. "A mixed methods approach to Schrödinger equation: Finite difference method and quartic B-spline based differential quadrature method." An International Journal of Optimization and Control: Theories & Applications (IJOCTA) 9, no. 2 (2019): 223–35. http://dx.doi.org/10.11121/ijocta.01.2019.00709.

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The present manuscript include, finite difference method and quartic B-spline based differential quadrature method (FDM-DQM) to obtain the numerical solutions for the nonlinear Schr¨odinger (NLS) equation. For this purpose, firstly Schrödinger equation has been converted into coupled real value differential equations and then they have been discretized using special type of classical finite difference method namely, Crank-Nicolson scheme. After that, Rubin and Graves linearization techniques have been utilized and differential quadrature method has been applied. So, partial differential equati

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Ahmad, Salman, Habib Ullah, T. Hayat, and A. Alsaedi. "Computational analysis of time-dependent viscous fluid flow and heat transfer." International Journal of Modern Physics B 34, no. 13 (2020): 2050141. http://dx.doi.org/10.1142/s0217979220501416.

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The flow of viscous fluid between two parallel plates is investigated. The applications of the magnetic field effect have been considered in the vertical direction to the plates. Velocity has been presented in the presence of suction and injection. The temperature equation is assisted with the Joule heating effect. One of the numerical techniques, that is, finite difference approach has been used to tackle the given partial differential system. This method results in a system of simple algebraic equations. The unknown function is analyzed inside the domain. In this technique of solution, a sys

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HOSSEININIA, M., M. H. HEYDARI, and Z. AVAZZADEH. "THE NUMERICAL TREATMENT OF NONLINEAR FRACTAL–FRACTIONAL 2D EMDEN–FOWLER EQUATION UTILIZING 2D CHELYSHKOV POLYNOMIALS." Fractals 28, no. 08 (2020): 2040042. http://dx.doi.org/10.1142/s0218348x20400423.

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This paper develops an effective semi-discrete method based on the 2D Chelyshkov polynomials (CPs) to provide an approximate solution of the fractal–fractional nonlinear Emden–Fowler equation. In this model, the fractal–fractional derivative in the concept of Atangana–Riemann–Liouville is considered. The proposed algorithm first discretizes the fractal–fractional differentiation by using the finite difference formula in the time direction. Then, it simplifies the original equation to the recurrent equations by expanding the unknown solution in terms of the 2D CPs and using the [Formula: see te

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Ashraf, Muhammad, Iram Iqbal, M. Masud, and Nazara Sultana. "Numerical Prediction of Natural Convection Flow in the Presence of Weak Magnetic Prandtl Number and Strong Magnetic Field with Algebraic Decay in Mainstream Velocity." Advances in Applied Mathematics and Mechanics 9, no. 2 (2017): 349–61. http://dx.doi.org/10.4208/aamm.2014.m616.

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AbstractIn present work, we investigate numerical simulation of steady natural convection flow in the presence of weak magnetic Prandtl number and strong magnetic field by involving algebraic decay in mainstream velocity. Before passing to the numerical simulation, we formulate the set of boundary layer equations with the inclusion of the effects of algebraic decay velocity, aligned magnetic field and buoyant body force in the momentum equation. Later, finite difference method with primitive variable formulation is employed in the physical domain to compute the numerical solutions of the flow

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Trom, J. D., and M. J. Vanderploeg. "Automated Linearization of Nonlinear Coupled Differential and Algebraic Equations." Journal of Mechanical Design 116, no. 2 (1994): 429–36. http://dx.doi.org/10.1115/1.2919397.

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This paper presents a new approach for linearization of large multibody dynamic systems. The approach uses an analytical differentiation of terms evaluated in a numerical equation formulation. This technique is more efficient than finite difference and eliminates the need to determine finite difference pertubation values. Because the method is based on a relative coordinate formalism, linearizations can be obtained for equilibrium configurations with non-zero Cartesian accelerations. Examples illustrate the accuracy and efficiency of the algorithm, and its ability to compute linearizations for

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Akers, Benjamin, Tony Liu, and Jonah Reeger. "A Radial Basis Function Finite Difference Scheme for the Benjamin–Ono Equation." Mathematics 9, no. 1 (2020): 65. http://dx.doi.org/10.3390/math9010065.

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A radial basis function-finite differencing (RBF-FD) scheme was applied to the initial value problem of the Benjamin–Ono equation. The Benjamin–Ono equation has traveling wave solutions with algebraic decay and a nonlocal pseudo-differential operator, the Hilbert transform. When posed on R, the former makes Fourier collocation a poor discretization choice; the latter is challenging for any local method. We develop an RBF-FD approximation of the Hilbert transform, and discuss the challenges of implementing this and other pseudo-differential operators on unstructured grids. Numerical examples, s

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Oliveira, F. De, S. R. Franco, and M. A. Villela Pinto. "The Effect of Multigrid Parameters in a 3D Heat Diffusion Equation." International Journal of Applied Mechanics and Engineering 23, no. 1 (2018): 213–21. http://dx.doi.org/10.1515/ijame-2018-0012.

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AbstractThe aim of this paper is to reduce the necessary CPU time to solve the three-dimensional heat diffusion equation using Dirichlet boundary conditions. The finite difference method (FDM) is used to discretize the differential equations with a second-order accuracy central difference scheme (CDS). The algebraic equations systems are solved using the lexicographical and red-black Gauss-Seidel methods, associated with the geometric multigrid method with a correction scheme (CS) and V-cycle. Comparisons are made between two types of restriction: injection and full weighting. The used prolong

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Jordan, Lewis, Ray Souter, Bernard Parresol, and Richard F. Daniels. "Application of the Algebraic Difference Approach for Developing Self-Referencing Specific Gravity and Biomass Equations." Forest Science 52, no. 1 (2006): 81–92. http://dx.doi.org/10.1093/forestscience/52.1.81.

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Abstract Biomass estimation is critical for looking at ecosystem processes and as a measure of stand yield. The density-integral approach allows for coincident estimation of stem profile and biomass. The algebraic difference approach (ADA) permits the derivation of dynamic or nonstatic functions. In this study we applied the ADA to develop a self-referencing specific gravity function and biomass function as part of a density-integral system composed of taper, volume, specific gravity, and biomass functions. This was compared to base systems of similar equations that did not have the self-refer

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Solovarova, Liubov S., and Ta D. Phuong. "On the numerical solution of second-order stiff linear differential-algebraic equations." Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva 24, no. 2 (2022): 151–61. http://dx.doi.org/10.15507/2079-6900.24.202202.151-161.

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This article addresses systems of linear ordinary differential equations with an identically degenerate matrix in the main part. Such formulations of problems in literature are usually called differential-algebraic equations. In this work, attention is paid to the problems of the second order. Basing on the theory of matrix pencils and polynomials, sufficient conditions for existence and uniqueness of the equations’ solution are given. To solve them numerically, authors investigate a multistep method and its version based on a reformulated notation of the original problem. This representation

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Liu, Fushou, and Dongping Jin. "A High-Efficient Finite Difference Method for Flexible Manipulator with Boundary Feedback Control." Space: Science & Technology 2021 (August 18, 2021): 1–10. http://dx.doi.org/10.34133/2021/9874563.

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The paper presents a high-efficient finite difference method for solving the PDE model of the single-link flexible manipulator system with boundary feedback control. Firstly, an abstract state-space model of the manipulator is derived from the original PDE model and the associated boundary conditions of the manipulator by using the velocity and bending curvature of the flexible link as the state variables. Then, the second-order implicit Crank-Nicolson scheme is adopted to discretize the state-space equation, and the second-order one-sided approximation is used to discretize the boundary condi

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